Volume 9, issue 1 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Periodic maps of composite order on positive definite 4–manifolds

Allan L Edmonds

Geometry & Topology 9 (2005) 315–339

arXiv: math.GT/0205110

Abstract

The possibilities for new or unusual kinds of topological, locally linear periodic maps of non-prime order on closed, simply connected 4–manifolds with positive definite intersection pairings are explored. On the one hand, certain permutation representations on homology are ruled out under appropriate hypotheses. On the other hand, an interesting homologically nontrivial, pseudofree, action of the cyclic group of order 25 on a connected sum of ten copies of the complex projective plane is constructed.

Keywords
periodic map, 4–manifold, positive definite, permutation representation, pseudofree
Mathematical Subject Classification 2000
Primary: 57S17
Secondary: 57S25, 57M60, 57N13
References
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Publication
Received: 8 July 2004
Revised: 23 January 2005
Accepted: 21 February 2005
Published: 23 February 2005
Proposed: Ronald Fintushel
Seconded: Walter Neumann, Ronald Stern
Authors
Allan L Edmonds
Department of Mathematics
Indiana University
Bloomington
Indiana 47405
USA